Determination of waveguide parameters

• US 7,110,900 B2
• Filed: 04/07/2004
• Issued: 09/19/2006
• Est. Priority Date: 04/11/2003
• Status: Active Grant

• Current Assignee: WesternGeco LLC
• Original Assignee: WesternGeco LLC
• Inventors: Adler, Frank, Muyzert, Everhard
• Primary Examiner(s): NGHIEM, MICHAEL P
• Application Number:
  US10/820,088
• Publication Number:
  US 20040230389A1
• Time in Patent Office: 895 Days
• Field of Search: 702/75, 702/76, 702170-172, 385/122, 385/123, 367/48, 367/49, 367/75, 73597-602
• US Class Current: 702/76
• CPC Class Codes: G01V 1/30 Analysis G01V1/50 takes precedence

Abstract

A method of determining at least one parameter of a waveguide (3) from wavefield data acquired from wave propagation in the waveguide including obtaining first and second dispersion curves (9a, 9b, 9c) in the frequency domain from the wavefield data. A frequency interval between the first dispersion curve and the second dispersion curve is found, and this is used in the determination of at least one parameter of the waveguide. The frequency separation Δƒ(V) between the first and second dispersion curves may be found at a particular value of the phase velocity V, and the thickness h of the waveguide can be found using:

$\Delta f\left(V\right)=\frac{c_1}{2h\sqrt{1-\frac{c_1^2}{V^2}}}$
Here, c₁ is the velocity of wave propagation in the waveguide. This may be found from the asymptotic velocity values of the dispersion curves.

Claims

1. A method of determining at least one parameter of a waveguide from wavefield data acquired from wave propagation in the waveguide, the method comprising the steps of:

obtaining a first and a second dispersion curves corresponding to different guided wave modes in the frequency domain from the wavefield data;

determining at least one parameter of the waveguide from a frequency interval between the first dispersion curve and the second dispersion curve;

obtaining the first and second dispersion curves in the frequency and phase velocity domain;

determining the velocity of wave propagation in the waveguide from the dispersion curves as the asymptotic velocity limit of the dispersion curves; and

storing the determined velocity of wave propagation.

2. A method as claimed in claim 1 comprising determining the frequency separation Δ

ƒ

(V) between the first and second dispersion curves at a first value of the phase velocity V.

3. A method as claimed in claim 2 comprising determining the thickness h of the waveguide using:

$\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br>\left(V\right)=\frac{c_1}{2<br><br>h<br><br>\sqrt{1-\frac{c_1^2}{V^2}}}$

where c₁ is the velocity of wave propagation in the waveguide.

4. A method as claimed in claim 1 comprising determining values of the frequency separation between the first dispersion curve and the second dispersion curve for at least two different values of the phase velocity.

5. A method as claimed in claim 4 comprising determining the thickness of the waveguide from the values of the frequency separation between the first dispersion curve and the second dispersion curve for at least two different values of the phase velocity.

6. A method as claimed in claim 4 comprising determining the thickness h of the waveguide using:

$h=\frac{c_1}{2<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br>\left(V\right)<br><br>\sqrt{1-\frac{c_1^2}{V^2}}}<br><br><br><br>\forall <br><br>V$

7. A method as claimed in claim 1 and comprising the step of auto-correlating in the frequency-velocity domain the first and second dispersion curves, and determining at least one parameter of the waveguide from the results of the auto-correlation step.

8. A method of processing wavefield data, the method comprising:

acquiring wavefield data;

determining at least one parameter of a waveguide according to a method of claim 1; and

taking the at least one parameter into account during subsequent processing of the wavefield data.

9. A method as claimed in claim 8 wherein the wavefield data are seismic wavefield data.

10. A method as claimed in claim 1 wherein the step of determining at least one parameter is independent of density of the waveguide.

11. A method as claimed in claim 10 wherein the step of determining at least one parameter is independent of density of a layer below the waveguide.

12. A method as claimed in claim 1 wherein the first and second dispersion curves are adjacent in the frequency domain and phase velocity domain.

13. A storage medium containing a program for controlling a programmable data processor to carry out a method as defined claim 1.

14. An apparatus for determining at least one parameter of a waveguide from wavefield data acquired from wave propagation in the waveguide, the apparatus comprising:

a processor for obtaining first and second dispersion curves corresponding to different guided wave modes in the frequency domain from the wavefield data;

a processor for determining at least one parameter of the waveguide from a frequency interval between the first dispersion curve and the second dispersion curve;

a calculator for obtaining first and second dispersion curves in the frequency and phase velocity domain;

a calculator for determining the velocity of wave propagation in the waveguide from the dispersion curves and wherein said apparatus

is adapted to determine the velocity of wave propagation in the waveguide as the asymptotic velocity limit of the dispersion curves.

15. An apparatus as claimed in claim 14 comprising a frequency separator for determining the frequency separation Δ

ƒ

(V) between the first and second dispersion curves at a first value of the phase velocity V.

16. An apparatus as claimed in claim 15 and comprising thickness meter for determining the thickness h of the waveguide using:

$\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br>\left(V\right)=\frac{c_1}{2<br><br>h<br><br>\sqrt{1-\frac{c_1^2}{V^2}}}$

where c₁ is the velocity of wave propagation in the waveguide.

17. An apparatus as claimed in claim 14 adapted to determine values of the frequency separation between the first dispersion curve and the second dispersion curve for at least two different values of the phase velocity.

18. An apparatus as claimed in claim 17 adapted to determining the thickness of the waveguide from the values of the frequency separation between the first dispersion curve and the second dispersion curve for at least two different values of the phase velocity.

19. An apparatus as claimed in claim 17 comprising means for determining the thickness h of the waveguide using:

$h=\frac{c_1}{2<br><br>\mathrm{\Delta <br><br>}<br><br><br><br>f<br><br>\left(V\right)<br><br>\sqrt{1-\frac{c_1^2}{V^2}}}<br><br><br><br>\forall <br><br>V$

20. An apparatus as claimed in claim 14 comprising correlator for auto-correlating, in the frequency-velocity domain, the first and second dispersion curves, and a calculator for determining at least one parameter of the waveguide from the output of the auto-correlation means.

21. An apparatus as claimed in claim 14 comprising a programmable data processor.

22. A storage medium containing a program for the data processor of an apparatus as defined in claim 21.

23. An apparatus as claimed in claim 14 wherein the processor for determining at least one parameter is independent of density of the waveguide.

24. An apparatus as claimed in claim 23 wherein the processor for determining at least one parameter is independent of density of a layer below the waveguide.

25. An apparatus as claimed in claim 14 wherein the first and second dispersion curves are adjacent in the frequency domain and phase velocity domain.